Pakistan Journal of Statistics and Operation Research
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A New Odd-Burr Pareto Distribution: Statistical Properties, Estimation, and Applications
No full textThis study introduces the Odd-Burr Pareto (OBu-P) distribution as a novel and flexible model, which is developed by combining the Burr and Pareto distributions using the T-X generator approach (Alizadeh et al. 2017). The OBu-P distribution can be used for modelling complex phenomenon characterized by heavy tails.
The paper provides the OBu-P distribution’s statistical properties, including its moments, incomplete moments, quantile functions, and limiting behaviours, as well as its generating functions and order statistics. Maximum likelihood estimation is applied to facilitate efficient parameter estimation of the OBu-P. The flexibility of distribution is shown in a real-life example versus its alternatives
A Generalized Exponential Regression Model for Predicting High-Grade Glioma Growth in Paediatric Patients
No full textHigh-grade gliomas (HGG) are invasive brain tumours characterized by abnormal growth patterns and poor prognoses. Aware and precise prediction of tumour growth helps improve both treatment protocols and patient medical outcome. The quick replicating and diverse nature of HGGs in children makes their predictive progression highly difficult to determine. This research utilized a generalized exponential regression approach to study glioma progression in children's brains with predicted accuracy reaching 73.68% for all tumours but elevating to 77.7% for small tumours under 100 mm³. Statistical analyses revealed significant negative correlations between tumour growth and tumour size, along with pre-radiotherapy performance status (PS Before RT), as determined by Kendall’s Tau test. The Mann-Whitney U and Kruskal-Wallis H tests were employed for bivariate analysis of categorical data, demonstrating a significant association (p < .05) among tumour growth rate, the extent of surgical resection, and survival status. The child's age, the occurrence of headaches, and edema were independently associated with the progression of tumour growth. These findings enhance the understanding of paediatric HGGs development, facilitating more accurate prognostic evaluations and improving personalized treatment strategies
Generalized Bayesian Double Group Sampling Plan for Manufacturing Industry
No full textQuality is not simply a goal or a choice for organizations, it is also a need for success in the global market. Acceptance sampling is one of two key strategies for quality assurance in manufacturing industry, along with statistical process control. After inspection the lot is either accepted or rejected based on the acceptance criteria. If historical information about the product is available, then the most effective approach for making the appropriate judgement is the Bayesian approach. To estimate quality regions, this work presents a Bayesian double group sampling plan (BDGSP). Based on acceptance criteria, the binomial distribution is used to build a likelihood function for defective and non-defective items. The beta distribution is utilized as the prior distribution to determine the average probability of acceptance. For some stated values of producer’s and consumer’s risks, four different quality regions are estimated. The suggested plan estimates variation point values based on various design parameter combinations. Producer's and consumer's risks correlate with acceptable quality levels and limiting quality levels of regions, respectively. Operating characteristic curves are used to monitor the effects of change in the values of specified parameters and for comparison with existing sampling plan. Application based on real data set proves that the proposed plan is applicable for existing manufacturing industry policies
Characterizations of Certain (2023-2024) Introduced Univariate Continuous Distributions
No full textThis paper deals with various characterizations of certain univariate continuous distributions proposed in (2023-2024). These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) the hazard function; (iii) reverse hazard function and (iv) conditional expectation of a single function of the random variable. It should be mentioned that for the characterization (i) the cumulative distribution function need not have a closed form and depends on the solution of a first order differential equation, which provides a bridge betweenprobability and differential equation
A New Cubic Transmuted Inverse Weibull Distribution: Theory and Applications
No full textThis paper introduces a new cubic transmutation of the inverse Weibull distribution, known as a cubic transmuted inverse Weibull distribution. The model is thought to be useful for the analysis of complex life data, modeling failure times, accessing product reliability, and many other fields like economics, hydrology, biology, and engineering. Some statistical features of the proposed distribution are explored. These include moments, generating functions, quantile functions, reliability functions, and hazard rate functions. The distribution of order statistics for the proposed cubic transmuted inverse Weibull distribution is also studied. The maximum likelihood estimation approach is used to estimate the model parameters. The effectiveness of the estimation is investigated through extensive simulation study. The suitability of the proposed distribution has been studied by using five real-life datasets. It is found that the proposed distribution is the most suitable fit for the used data sets
Characterizations of the Recently Introduced Discrete Distributions
No full textCertain characterizations of 26 recently introduced discrete distributions are presented in three directions: (i) based on an appropriate function of the random variable; (ii) in terms of the reverse hazard function and (iii) in terms of the hazard function
Sample size determination when the parameter of interest is the coefficient of variation under normality for the data
No full textThis study considers classical and Bayesian inference approaches for the coefficient of variation under normality for the data, especially on the determination of the sample size of a random sample needed in a second stage of an experiment. This topic has been explored by many authors in the last decades. The first goal of the study is to present simple formulations to get the inferences of interest for the coefficient of variation under normality and usual frequentist approach based on the asymptotic normality of the maximum likelihood estimators for the mean and standard deviation of the normal distribution and using the delta method to get the inferences of interest for the coefficient of variation. Simple hypothesis tests and determination of the sample size are discussed under the frequentist approach.The second goal of the study is to present a sample size determination under a Bayesian approach, where it is assumed a Jeffreys non-informative prior distribution of the parameters of the normal distribution assumed for the data and using standard Markov Chain Monte Carlo (MCMC) methods to get the posterior summaries of interest
Detection of Outliers Method in Grouped Multivariate Data: A Method Based on Multiple Linear Regression
No full textCluster analysis is applied to group data so that samples within the same group are similar. A common problem with multivariate data implementation is that the data differs significantly from most of the other data. Outliers can significantly impact data analysis and model performance, making their detection crucial in various domains. This study presents an investigation of the outlier detection method using multiple linear regression for grouped multivariate data. The research compares the performance of the proposed method with two existing approaches, namely the Caroni and Billor (2007) method and the Hardin and Rocke (2004) method. In the case of uncontaminated data, the proposed method demonstrates a high percentage of detected outliers as the number of variables and sample size increase, indicating its effectiveness in outlier identification. In the scenario of contaminated data, the results reveal that the proposed method consistently outperforms both the Caroni and Billor method and the Hardin and Rocke method in terms of accuracy and precision. These findings highlight the effectiveness of the proposed method for outlier detection in grouped multivariate data. The study contributes to the existing knowledge of outlier detection approaches and provides insights into their performance under different data conditions. Researchers and practitioners can benefit from these findings when selecting appropriate outlier detection methods for various applications
Topp-Leone generalization of the Generalized Pareto distribution and its impact on Extreme value modelling
No full textExtreme Value theory (EVT) is a phenomenon used to model rare or extreme events and has been useful in well-known areas such as finance, economics, hydrology, insurance, etc. In this paper, we combine EVT and Bayesian statistics to estimate the extreme value index and other distribution parameters. EVT studies the behavior of the tails of the distribution, while Bayesian statistics allows us to incorporate prior knowledge of the parameters. The interdependence between these two statistical branches allows us to account for uncertainty in parameter and tail estimation. Block maxima and Peaks over Threshold are EVT divisions that are used to model observations. In this paper we use the Peaks over Threshold approach. The generalized Pareto distribution is a Peaks over Threshold distribution. Existing literature studied the generalizations and extensions of the generalized Pareto distribution. These extensions mostly focus on the positive domain of attraction. In this paper we contribute to the study of EVT by considering both the negative and positive domains of attraction. We consider the (Topp and Leone, 1955) generalization for the generalized Pareto distribution. We show, by means of a simulation study, that this distribution can effectively estimate the extreme value index and that it is less sensitive to threshold selection than the normal generalized Pareto distribution
A new class of probability distributions with an application in engineering science
No full textIn this manuscript, we introduced a new class of probability distributions called new exponentiated transformation(NET) that adds more flexibility to any baseline distribution without adding the complexity of an extra parameter. NET is then specialised on exponentiated exponential distribution and a new exponentiated exponential( NEE) distribution is obtained. The NEE distribution has wider flexibility in terms of density function and also has increasing, decreasing and bathtub hazard rate function. Several mathematical properties of NEE distribution are also highlighted. For applicability of proposed distribution, two engineering data sets are considered and it is sensed that NEE leads to a better fit than all models taken under consideratio